Finite Group Databasebeta

← Group #129484

Character table — Group #129484

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222224444444444444444888888161616161616161616161616161616161616161616161616
order12222244442244444444444444444444224444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ6111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ7111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ911111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ1011111111111111-1-1-1-111111111-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111
χ1111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ1211111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-111-1-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222-2-2-2-2222222-2-222-2-2-2-222-2-2000000000000000000000000
χ182222222222-2-2-2-22222-2-222-2-222-2-2-2-222000000000000000000000000
χ192222222222-2-2-2-2-2-2-2-222-2-222-2-222-2-222000000000000000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2000000000000000000000000
χ21222222-2-2-2-222-2-2000022-2-2-2-2220000002-2002-2000000000000000000
χ22222222-2-2-2-222-2-2000022-2-2-2-222000000-2200-22000000000000000000
χ23222222-2-2-2-222-2-20000-2-22222-2-20000002-200-22000000000000000000
χ24222222-2-2-2-222-2-20000-2-22222-2-2000000-22002-2000000000000000000
χ25222222-2-2-2-2-2-22200002222-2-2-2-2000000002-2002-20000000000000000
χ26222222-2-2-2-2-2-22200002222-2-2-2-200000000-2200-220000000000000000
χ27222222-2-2-2-2-2-2220000-2-2-2-22222000000002-200-220000000000000000
χ28222222-2-2-2-2-2-2220000-2-2-2-2222200000000-22002-20000000000000000
χ2922-2-22-222-2-22-22-200002i−2i2i−2i2i−2i2i−2i0000000000000000000000002ζ3−2ζ3002ζ−2ζ
χ3022-2-22-222-2-22-22-200002i−2i2i−2i2i−2i2i−2i000000000000000000000000−2ζ32ζ300−2ζ2ζ
χ3122-2-22-222-2-22-22-20000−2i2i−2i2i−2i2i−2i2i0000000000000000000000002ζ−2ζ002ζ3−2ζ3
χ3222-2-22-222-2-22-22-20000−2i2i−2i2i−2i2i−2i2i000000000000000000000000−2ζ2ζ00−2ζ32ζ3
χ3322-2-22-222-2-2-22-2200002i−2i−2i2i2i−2i−2i2i00000000000000000000002ζ−2ζ002ζ3−2ζ300
χ3422-2-22-222-2-2-22-2200002i−2i−2i2i2i−2i−2i2i0000000000000000000000−2ζ2ζ00−2ζ32ζ300
χ3522-2-22-222-2-2-22-220000−2i2i2i−2i−2i2i2i−2i00000000000000000000002ζ3−2ζ3002ζ−2ζ00
χ3622-2-22-222-2-2-22-220000−2i2i2i−2i−2i2i2i−2i0000000000000000000000−2ζ32ζ300−2ζ2ζ00
χ3722-2-22-2-2-2222-2-2200002i−2i−2i2i−2i2i2i−2i00000000000000002ζ−2ζ002ζ3−2ζ300000000
χ3822-2-22-2-2-2222-2-2200002i−2i−2i2i−2i2i2i−2i0000000000000000−2ζ2ζ00−2ζ32ζ300000000
χ3922-2-22-2-2-2222-2-220000−2i2i2i−2i2i−2i−2i2i00000000000000002ζ3−2ζ3002ζ−2ζ00000000
χ4022-2-22-2-2-2222-2-220000−2i2i2i−2i2i−2i−2i2i0000000000000000−2ζ32ζ300−2ζ2ζ00000000
χ4122-2-22-2-2-222-222-200002i−2i2i−2i−2i2i−2i2i000000000000002ζ−2ζ002ζ3−2ζ30000000000
χ4222-2-22-2-2-222-222-200002i−2i2i−2i−2i2i−2i2i00000000000000−2ζ2ζ00−2ζ32ζ30000000000
χ4322-2-22-2-2-222-222-20000−2i2i−2i2i2i−2i2i−2i000000000000002ζ3−2ζ3002ζ−2ζ0000000000
χ4422-2-22-2-2-222-222-20000−2i2i−2i2i2i−2i2i−2i00000000000000−2ζ32ζ300−2ζ2ζ0000000000
χ454444-4-44-44-4000000000000000000004i−4i000000000000000000000000
χ464444-4-44-44-400000000000000000000−4i4i000000000000000000000000
χ474444-4-4-44-440000000000000000004i−4i00000000000000000000000000
χ484444-4-4-44-44000000000000000000−4i4i00000000000000000000000000
χ4944-4-4-444-4-4400004i4i−4i−4i00000000000000000000000000000000000000
χ5044-4-4-444-4-440000−4i−4i4i4i00000000000000000000000000000000000000
χ5144-4-4-44-444-400000000000000004i−4i0000000000000000000000000000
χ5244-4-4-44-444-40000000000000000−4i4i0000000000000000000000000000
χ538-88-800000000004i−4i4i−4i00000000000000000000000000000000000000
χ548-88-80000000000−4i4i−4i4i00000000000000000000000000000000000000
χ558-8-8800000000004-4-4400000000000000000000000000000000000000
χ568-8-880000000000-444-400000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.